Question: Simplify the following expression: $k = \dfrac{-3x^2 - 9x + 54}{x + 6} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ k =\dfrac{-3(x^2 + 3x - 18)}{x + 6} $ Then we factor the remaining polynomial: $x^2 + {3}x {-18} $ ${6} {-3} = {3}$ ${6} \times {-3} = {-18}$ $ (x + {6}) (x {-3}) $ This gives us a factored expression: $\dfrac{-3(x + {6}) (x {-3})}{x + 6}$ We can divide the numerator and denominator by $(x - 6)$ on condition that $x \neq -6$ Therefore $k = -3(x - 3); x \neq -6$